Someone said you could use a normal bitcoin wallet address for counterparty, but you must own the wallet, so you cannot use a bitcoin address from an exchange.
Do we still have to download a counterparty client to use it?
Yes, right now you need to download Bitcoin-QT and the Counterparty client to use it.
There is a Counterparty webwallet, which is currently on the Testnet right now. By April 5th, we should have the WebWallet on the mainnet.